122 Basic Concepts of the Theory of Difference SchemesLikewise, one can prove another inequalityBy the same token,y^2 (x;) < ~ (1 + E) (y; + y~) + ~ ( 1 + ~) ( 1, y~],
I [y] 12 < ~ (1 + E) (y; + y~) + ~ ( 1 + ~) ( 1, y~].
Putting E = c 1 and using the identity
(12)we establish relation (11).
It is plain to deduce for the norm of the operator A the estimate(13) 11 A 11 < h 4 ( 2 1 + 2 1 C2 h) ' where
Indeed 'andwhere I [y] 12 = L;:~^1 YI h + ~ h ( y; + y~ ). By virtue of the relations
[Ay, y] < llAll · l[Y]l^2 ,
we get from (12) the desired estimate (13).